BOAC,
There's still a difference between "executing" and "installing".
My kids can run programs but sure as hell can't install any (normal user accounts).
Remember that applications that execute do so with the security privileges of the account running them.
A nasty may run while they are logged in, but can't install itself (other than to areas to which they have write access (their own profiles), so a reboot later they are not there for any other user.
I had exactly this problem as a short while ago one child had gotten one of these anti-malware nasties - problem solved by deleting their account (of course data was already backed up).
PC otherwise clean (Sophos, Spybot and Anti-malwarebytes sweeps clean).
SD